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Modeling Climate Change Through Mathematical Collaboration

There are no simple solutions for the mathematical problems Mary Lou Zeeman is trying to solve. She is looking at some of the most puzzling and pressing sustainability problems facing the world.

How much will sea level rise as ice sheets melt? How do human activities affect climate change? And how do we balance socio-economic needs and the environment?

Zeeman, Bowdoin's R. Wells Johnson Professor of Mathematics, is spearheading three National Science Foundation (NSF)-funded collaborations that are paving new pathways between mathematicians and scientists working on the frontlines of climate-change research.

"There are plenty of climate scientists doing sophisticated climate modeling but there have been very few mathematicians involved in that effort," notes Zeeman. "It seemed like a great shame that we had so many untapped resources and other ways of thinking of mathematical models that could be brought to bear on the challenges scientists have been facing."

There is also the flip side. Advanced mathematical tools may be new to many climate scientists, but bodies of scientific knowledge are usually foreign territory for most mathematicians.

One of the ways Zeeman is helping to address these issues is through development of a Climate Math Web Portal, which launches in 2011. The Web Portal will provide resources about the mathematical challenges in climate science to mathematicians who want to apply their expertise to questions of climate science, or integrate climate examples into their classes.

"You have to invest quite a lot of time to learn each others' language," notes Zeeman, who made that discovery earlier in her career, when she undertook pioneering research in mathematic modeling of the menstrual cycle. (Read about her biomathematical research.)

The challenge can be even more confusing when the same word is used by both disciplines, yet has distinct meanings, she says:

"To a mathematician, for example, the word 'linear' has a very strict meaning. It is a straight line," says Zeeman. "But in biology you talk about linear graphs that may or may not be straight ... It's more about being able to use changes in the observed output to determine changes in the input with reasonable accuracy. It's not so absolute. Similarly, the word 'hypothesis' has a different meaning in math than in most sciences. In mathematics it's something you assume, in biology it's something you test."

Zeeman's newest project is perhaps her most ambitious and wide reaching. She is working with a multidisciplinary team of researchers from 12 universities around the nation to develop a virtual climate mathematics center.

Zeeman and the other mathematicians in the Mathematics and Climate Research Network (MCRN) will work directly with climate scientists from leading laboratories, including the National Center for Atmospheric Research and Los Alamos National Laboratory, to model climate processes, investigate dynamics of climate, and reconstruct and analyze historical climate data.

"Many processes relevant to climate change remain poorly understood and modeled," observes Zeeman, "because they evolve over disparate time scales, ranging from minutes to millenia, and they interact in multiple ways. Among these are sea-ice structure, ocean circulation, cloud formation, and extreme weather, such as hurricanes, tornadoes and flooding. ... And, of course, we are far from including human behavior and biological adaptation in climate-change models.

"One has to have hope and to remember that, at some level, the planet will be okay.

"Mathematical formulas can describe microstructures in natural systems and they also can model tipping points, and chaos. Both are fundamental to developing realistic hypotheses about climate processes and can help us extrapolate into the future."

Issues of biodiversity and human interaction are an integral part of another of Zeeman's NSF-backed initiatives. She helped to found the Institute for Computational Sustainability, based at Cornell University, which is developing computational methods—combining optimization, machine learning and dynamical systems—to tackle some key environmental, economic and societal aspects of sustainability. The research team brings together computer scientists, mathematicians, economists, biologists and environmental scientists.

As daunting and unpredictable as these issues are, Zeeman says she is encouraged that positive change is possible: "One has to have hope and to remember that, at some level, the planet will be okay. We humans do have some choice in the future we create for ourselves and for biodiversity. I believe that whatever your talent and your passion, you can use them to help the planet," she says. "You don't have to change who you are to do that. But it's difficult to justify not trying."

Zeeman has been awarded four research grants from the NSF since joining the Bowdoin faculty in 2006. The NSF is providing $1 million a year for five years to support the Mathematics and Climate Research Network, and $2 million a year for five years to support the Institute for Computational Sustainabilty.

"Students and post-docs are the life-blood of these research efforts," notes Zeeman. "There are wonderful opportunities for student research in all the current projects."